Problem: The sum of two numbers is $94$, and their difference is $72$. What are the two numbers?
Solution: Let $x$ be the first number, and let $y$ be the second number. The system of equations is: ${x+y = 94}$ ${x-y = 72}$ Solve for $x$ and $y$ using elimination. Add the top and bottom equations together. $ 2x = 166 $ $ x = \dfrac{166}{2} $ ${x = 83}$ Now that you know ${x = 83}$ , plug it back into $ {x+y = 94}$ to find $y$ ${(83)}{ + y = 94}$ ${y = 11}$ You can also plug ${x = 83}$ into $ {x-y = 72}$ and get the same answer for $y$ ${(83)}{ - y = 72}$ ${y = 11}$ Therefore, the larger number is $83$, and the smaller number is $11$.